What is the range of the function y = -x2 + 1?

To solve this problem you must apply the proccedure shown below:

 1- You have the following function given in the problem above:

 y=-x² + 1

 2- If you graph the function, you will obtain the parabola shown in the figure attached. As you can see, the vertex is ( the maximum value of y is y coordinate of the vertex is (0,1) and the parabola opens down. Therefore the range is:

 Range: {y∈R:y≤1}

 Therefore, the answer is: {y∈R:y≤1}